CN110197040B - Reynolds number-based annular pressure calculation method - Google Patents
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Abstract
The invention relates to an annulus pressure calculation method based on Reynolds number, comprising the following steps: 1. collecting basic parameters of the injection and production well through field test or experiment; 2. calculating the lower leakage flow of the annular protection fluid of the injection and production well; 3. calculating the radius of primary bubbles when the channeling gas is separated from the surface of the cement ring; 4. judging the Reynolds number of the bubbles, and selecting different bubble rising speed models according to the Reynolds number; 5. computing annulus protectionThe rising speed of the gas in the liquid; step six: calculating the value of the annulus pressure, wherein the calculation of the annulus pressure is an iterative process, and after the rising speed of bubbles at a certain time is known, the annulus pressure at the moment is solved; after obtaining the annular pressure at the initial time i =1, ifP f ＝P c And finishing the calculation; if it isP f ≠P c I = i +1, and the step two is returned until the calculation is repeatedP f ＝P c . The invention considers the influence of Reynolds number on the rising speed of the bubbles, and the calculated annular pressure value can more scientifically reflect the actual rising condition of the annular pressure.
Description
The technical field is as follows:
the invention relates to a shaft integrity evaluation technology, in particular to an annulus pressure calculation method based on a Reynolds number.
Background art:
the annular pressure not only can influence the injection and production effects of the injection and production well, but also can seriously influence the production safety. Because the gas is more active, the phenomenon of annulus pressure of the gas well is more common. According to statistics, more than 43% of wells outside the gulf of Mexico in the United states have the phenomenon of annular pressure; the Chinese Tarim oil field has more than 93% of annulus pressure of a high-pressure gas well, and the highest annulus pressure value even exceeds 50MPa. The annulus pressure provides a serious challenge for the safe production of the injection and production well, so that an accurate annulus pressure calculation method is necessary to be adopted for controlling the annulus pressure phenomenon to realize the accurate prediction of a pressure value, so that the control of the annulus pressure phenomenon is guided, and the integrity of a shaft of the injection and production well is guaranteed.
The existing annular pressure calculation methods are mainly divided into the following two types:
(1) Ignoring the migration change of gas in the annular protection fluid, only considering the gas channeling in the cement ring and the accumulation at the gas cap.
The calculation method considers that the cement sheath is a porous medium with uniform texture, the leakage flow entering the annular space protection liquid from the cement sheath is obtained by utilizing the Darcy formula, the leakage flow is taken as the gas flow finally entering the gas cap, and then the annular space pressure value is obtained through iterative calculation of a PVT state equation. The method can calculate the rising condition of the annular pressure at different time, but after the channeling gas enters the annular protection liquid, the migration state of the gas in the annular protection liquid changes, which causes the difference between the leakage flow at the lower part of the annular protection liquid and the gas flow entering the gas cap at the upper part. Because the calculation method ignores the migration change of gas in the annular protection liquid, the volume of the gas entering the gas cap in unit time is not consistent with the actual condition, and the finally calculated annular pressure value cannot reflect the real pressure of the annulus, the calculation method is only suitable for the condition that the well cementation cement slurry returns to the ground.
(2) Consider the change in the migration state of the blow-by gas in the annular protection fluid.
The method can calculate the annular pressure under the condition that the cement paste is not returned to the ground. The calculation method is to describe a change rule of the migration speed of gas in the annular protection liquid, supposing that the floating of the channeling gas in the annular protection liquid belongs to bubble flow, establishing a balance equation through stress analysis of a single bubble, and determining the rising speed of the final bubble entering the gas cap based on the equation. Compared with a calculation method without considering migration change of gas in the annular protection liquid, the calculation method is more consistent with underground practical characteristics. However, this type of calculation method still has disadvantages:
first, the bubble Reynolds numbers of the cross-flow gas will be different under different conditions. When the Reynolds number of the bubbles is less than 1, the bubbles rise in a spherical shape, and the appearance hardly changes in the rising process; secondly, when the Reynolds number of the bubbles is more than 1, the bubbles are easy to change from a spherical shape to a cap shape in the rising process. Because the shape of the bubbles directly influences the migration speed in the rising process, the calculation method cannot distinguish and calculate the rising speeds of the bubbles with different Reynolds numbers, and therefore the existing calculation method cannot accurately predict the rising rule of the annular pressure.
The annular pressure in the service process of the injection and production well cannot be avoided, and in order to truly evaluate the annular pressure degree of the casing, a calculation method which is closer to the flowing rule of gas in annular protection needs to be provided.
The invention content is as follows:
the invention aims to provide an annular pressure calculation method based on a Reynolds number, which is used for solving the problem that the existing calculation method cannot accurately predict the rising rule of the annular pressure.
The technical scheme adopted by the invention for solving the technical problems is as follows: the method for calculating the annular pressure based on the Reynolds number comprises the following steps:
the method comprises the following steps: collecting basic parameters of an injection and production well through field tests or experiments, wherein the basic parameters comprise: temperature and pressure of a stratum, porosity of a cement sheath, permeability of the cement sheath, temperatures of a wellhead and a shaft, related physical parameters of an annular protection fluid and related physical parameters of a channeling gas;
step two: calculating leakage flow q at lower part of injection and production well annular protection liquid g ：
In the formula: k is the permeability of the cement sheath, m 2 (ii) a A is the annular cross-sectional area, m 2 ；T sc Standard condition temperature, K; mu.s g Is gas phase viscosity, pas; t is f Is the formation temperature, K; l is a radical of an alcohol f Is the cement sheath length, m; p is sc Is standard condition pressure, pa; p f Is the formation pressure, pa; p is c The lower part surface pressure of the annular protection liquid is Pa.
Step three: calculating the radius r of the primary bubble when the channeling gas is separated from the surface of the cement ring b ：
In the formula: rho l Is the density of annular protection liquid, kg/m 3 ；ρ g Is the density of the gas in the cross flow, kg/m 3 (ii) a g is the acceleration of gravity, 9.8m/s 2 ；μ l Viscosity of annular protecting liquidPa · s; sigma is the surface tension coefficient of the annular space protection liquid and the gas, N/m; phi is the porosity of the cement sheath, and is dimensionless;
is the cement particle diameter, m.
Step four: judging the bubble Reynolds number, and selecting different bubble rising speed models according to the Reynolds number; the bubble Reynolds number equation is:
(1) when the Reynolds number Re of the bubbles is less than 1, a small Reynolds number bubble rising speed calculation formula is selected:
in the formula: c D As a resistance coefficient, its value was 24/Re.
(2) When the Reynolds number Re of the bubble is more than 1, a calculation formula of the rising speed of the bubble with a large Reynolds number is selected:
step five: calculating the rising velocity v of the gas in the annular space protection liquid t,w ：
Wherein:
a 3 ＝-(a 1 +a 2 +a 4 )
Step six: calculating the annulus pressure value P t ：
In the formula: v m Volume of annular space protection fluid, m 3 ；V t Is the gas cap volume, m 3 ；C m Is the compression coefficient of the annular space protection fluid Pa -1 ；T wh Well head temperature, K; a is the annular cross-sectional area, m 2 ；T wb Is the wellbore temperature, K; l is a radical of an alcohol f Is the annular space protection liquid height, m.
The calculation of the annular pressure is an iterative process, and after the rising speed of bubbles at a certain time is obtained, the annular pressure at the moment is solved; determining the annular pressure P at the initial time i =1 t 1 Then, if P f ＝P c If so, ending the calculation; if P f ≠P c And if i = i +1, returning to the step two for recalculating until the formation pressure P f Pressure P of lower part of annular protection liquid c Are equal.
The invention has the following beneficial effects:
(1) The influence of Reynolds number on the rising speed of the bubbles is considered, the Reynolds number of the bubbles of the channeling flow is taken as an evaluation index, and the calculated annular pressure value can more scientifically reflect the actual rising condition of the annular pressure;
(2) The method can perform sensitivity analysis on a plurality of parameters influencing annular pressure, and realizes optimization of engineering parameters based on the change rule of the annular pressure value under different conditions;
(3) The annular pressure calculation method provided by the invention has general applicability, and can determine reasonable pressure relief time according to the annular pressure dynamic curve, thereby providing guarantee for the integrity of the shaft of the injection and production well.
Detailed Description
The invention is further illustrated below:
the method for calculating the annular pressure based on the Reynolds number comprises the following steps:
the method comprises the following steps: collecting basic parameters of injection and production wells through field tests or experiments, comprising: temperature and pressure of the formation, porosity of the cement sheath, permeability of the cement sheath, temperature of the wellhead and the shaft, related physical parameters of the annular protection fluid and related physical parameters of the channeling gas;
step two: calculating leakage flow q at lower part of annular protection liquid of injection and production well g ：
In the formula: k is the permeability of the cement sheath, m 2 (ii) a A is annular cross-sectional area, m 2 ；T sc Standard condition temperature, K; mu.s g Is gas phase viscosity, pas; t is f Is the formation temperature, K; l is f Is the cement sheath length, m; p sc Is standard condition pressure, pa; p is f Is the formation pressure, pa; p c The pressure of the lower part of the annular protection liquid is Pa.
Step three: calculating the radius r of the primary bubble when the channeling gas is separated from the surface of the cement ring b ：
In the formula: ρ is a unit of a gradient l Is the density of annular protection liquid in kg/m 3 ；ρ g Is blow-by gasBulk density, kg/m 3 (ii) a g is the acceleration of gravity, 9.8m/s 2 ；μ l The viscosity of the annular protection fluid is Pa.s; sigma is the surface tension coefficient of the annular protection liquid and the gas, N/m; phi is the porosity of the cement sheath and is dimensionless;
is the cement particle diameter, m.
Step four: judging the Reynolds number of the bubbles, and selecting different bubble rising speed models according to the Reynolds number; the bubble reynolds number equation is:
(1) when the Reynolds number Re of the bubbles is less than 1, a small Reynolds number bubble rising speed calculation formula is selected:
in the formula: c D As a resistance coefficient, its value was 24/Re.
(2) When the Reynolds number Re of the bubble is more than 1, a calculation formula of the rising speed of the bubble with a large Reynolds number is selected:
step five: calculating the rising speed v of the gas in the annular protection liquid t,w ：
Wherein:
a 3 ＝-(a 1 +a 2 +a 4 )
in the formula: alpha is gas content and is dimensionless; n is a fluidity index and is dimensionless.
Step six: calculating the annulus pressure value P t ：
In the formula: v m Volume of annular space protection fluid, m 3 ；V t Is the gas cap volume, m 3 ；C m Is the compression coefficient of the annular space protection fluid Pa -1 ；T wh Is the well head temperature, K; a is the annular cross-sectional area, m 2 ；T wb Is the wellbore temperature, K; l is a radical of an alcohol f Is the annular protection liquid height, m.
The calculation of the annular pressure is an iterative process, and after the rising speed of bubbles at a certain time is known, the annular pressure at the moment is solved; determining the annular pressure P at the initial time i =1 t 1 Then, if P f ＝P c If so, ending the calculation; if P f ≠P c And i = i +1, and the calculation is returned to the step two to be recalculated until the formation pressure P f Pressure P of lower part of annular protection liquid c And are equal.
The method respectively calculates the migration speed of the bubbles under different Reynolds number conditions, more accords with the real migration rule of the gas in the annular protecting liquid, and accurately describes the rising condition of the pressure in each time period during the annular pressure recovery period, thereby guiding the formulation of annular pressure diagnosis and shaft integrity remedial measures and delaying the harm of annular pressure to safety production.
Claims (1)
1. An annular pressure calculation method based on Reynolds number is characterized in that:
the method comprises the following steps: collecting basic parameters of an injection and production well through field tests or experiments, wherein the basic parameters comprise: temperature and pressure of the formation, porosity of the cement sheath, permeability of the cement sheath, temperature of the wellhead and the shaft, related physical parameters of the annular protection fluid and related physical parameters of the channeling gas;
step two: calculating leakage flow q at lower part of annular protection liquid of injection and production well g ：
In the formula: k is the permeability of the cement sheath, m 2 (ii) a A is the annular cross-sectional area, m 2 ；T sc Standard condition temperature, K; mu.s g Gas phase viscosity, pas; t is f Is the formation temperature, K; l is a radical of an alcohol f Is the cement sheath length, m; p is sc Is standard condition pressure, pa; p is f Is the formation pressure, pa; p c The lower part surface pressure of the annular protection liquid is Pa;
step three: calculating the radius r of the primary bubble when the channeling gas is separated from the surface of the cement ring b ：
In the formula: rho l Is the density of annular protection liquid, kg/m 3 ；ρ g Is the density of the blow-by gas in kg/m 3 (ii) a g is gravitational acceleration of 9.8m/s 2 ；μ l The viscosity of the annular protection fluid is Pa.s; sigma is the surface tension coefficient of the annular space protection liquid and the gas, N/m; phi is the porosity of the cement sheath and is dimensionless;
is the cement particle diameter, m;
step four: judging the bubble Reynolds number, and selecting different bubble rising speed models according to the Reynolds number; the bubble Reynolds number equation is:
(1) when the Reynolds number Re of the bubbles is less than 1, a small Reynolds number bubble rising speed calculation formula is selected:
in the formula: c D Is a resistance coefficient, and the value is 24/Re;
(2) when the Reynolds number Re of the bubble is more than 1, a calculation formula of the rising speed of the bubble with a large Reynolds number is selected:
step five: calculating the rising velocity v of the gas in the annular space protection liquid t,w ：
Wherein:
a 3 ＝-(a 1 +a 2 +a 4 )
in the formula: alpha is gas content and is dimensionless; n is a fluidity index and is dimensionless;
step six: calculating the annulus pressure value P t ：
In the formula: v m Volume of annular protection fluid, m 3 ；V t Is the gas cap volume, m 3 ；C m Is the compression coefficient of the annular space protection fluid Pa -1 ；T wh Is the well head temperature, K; a is annular cross-sectional area, m 2 ；T wb Is the wellbore temperature, K; l is a radical of an alcohol f Is the annular space protection liquid height, m;
the calculation of the annular pressure is an iterative process, and after the rising speed of bubbles at a certain time is known, the annular pressure at the moment is solved; determining the annular pressure P at the initial time i =1 t 1 Then, if P f ＝P c If yes, the calculation is finished; if P f ≠P c And if i = i +1, returning to the step two for recalculating until the formation pressure P f Pressure P of lower part of annular protection liquid c Are equal.
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